Consider the specific heats

CH2O(s) = 2.09 J/g ¡¤◦ C. CH2O(§¤) =4.18 J/g ¡¤◦ C. CH2O(g) = 2.03 J/g ¡¤◦ C.
The heat of fusion for water is 334 J/g and the heat of vaporization for water is 2260 J/g. Calculate the amount of heat absorbed when 86 g of steam at 133◦C are completely converted to ice at −27◦C.
Answer in units of kJ

An easy but long problem.

You have two formulas to use for this.
Within a phase (all gas, all liquid, all solid),
q = mass x specific heat x (Tfinal-Tinitial)

At a transition point:
At the boiling point is is
q = mass x heat vaporization

At the melting point it is
q = mass x heat fusion.

Then add the qs for the total.

To calculate the amount of heat absorbed when 86 g of steam at 133°C is completely converted to ice at -27°C, we need to consider the following steps:

1. Calculate the heat absorbed to cool the steam from 133°C to 0°C.
2. Calculate the heat absorbed during the change of phase from steam at 100°C to ice at 0°C.
3. Calculate the heat absorbed to cool the ice from 0°C to -27°C.

Let's calculate each step:

Step 1: Calculate the heat absorbed to cool the steam from 133°C to 0°C.
The specific heat of steam to cool it from 133°C to 0°C is 2.03 J/g ◦C.
The difference in temperature is 133°C - 0°C = 133°C.

Heat absorbed = mass * specific heat * change in temperature
Heat absorbed = 86 g * 2.03 J/g ◦C * 133°C
Heat absorbed = 23092.78 J

Step 2: Calculate the heat absorbed during the change of phase from steam at 100°C to ice at 0°C.
The heat of vaporization for water is 2260 J/g.

Heat absorbed = mass * heat of vaporization
Heat absorbed = 86 g * 2260 J/g
Heat absorbed = 194360 J

Step 3: Calculate the heat absorbed to cool the ice from 0°C to -27°C.
The specific heat of ice to cool it from 0°C to -27°C is 2.09 J/g ◦C.
The difference in temperature is 0°C - (-27°C) = 27°C.

Heat absorbed = mass * specific heat * change in temperature
Heat absorbed = 86 g * 2.09 J/g ◦C * 27°C
Heat absorbed = 4802.82 J

Now, let's calculate the total heat absorbed by summing up the heat absorbed in each step:

Total heat absorbed = Heat absorbed in step 1 + Heat absorbed in step 2 + Heat absorbed in step 3
Total heat absorbed = 23092.78 J + 194360 J + 4802.82 J
Total heat absorbed = 222255.6 J

Finally, to convert the answer to kilojoules (kJ), we divide by 1000:
Total heat absorbed = 222255.6 J / 1000
Total heat absorbed ≈ 222.26 kJ

Therefore, the amount of heat absorbed when 86 g of steam at 133°C are completely converted to ice at -27°C is approximately 222.26 kJ.